Stability for semidiscrete Galerkin approximation of neutral delay equations

2008 ◽  
Author(s):  
R.H. Fabiano ◽  
J. Turi
Keyword(s):  
Galerkin Approximation ◽  
Delay Equations ◽  
Neutral Delay

Stability of Human Balance With Reflex Delays Using Galerkin Approximations

2015 ◽  
Vol 11 (4) ◽  
Author(s):  
Zaid Ahsan ◽  
Thomas K. Uchida ◽  
Akash Subudhi ◽  
C. P. Vyasarayani
Keyword(s):  
Differential Equation ◽  
Galerkin Approximation ◽  
The Elderly ◽  
Double Pendulum ◽  
Neutral Delay ◽  
Stability Margins ◽  
Human Balance ◽  
The Stability ◽  
The Galerkin Method ◽  
Delay Differential

Falling is the leading cause of both fatal and nonfatal injury in the elderly, often requiring expensive hospitalization and rehabilitation. We study the stability of human balance during stance using inverted single- and double-pendulum models, accounting for physiological reflex delays in the controller. The governing second-order neutral delay differential equation (NDDE) is transformed into an equivalent partial differential equation (PDE) constrained by a boundary condition and then into a system of ordinary differential equations (ODEs) using the Galerkin method. The stability of the ODE system approximates that of the original NDDE system; convergence is achieved by increasing the number of terms used in the Galerkin approximation. We validate our formulation by deriving analytical expressions for the stability margins of the double-pendulum human stance model. Numerical examples demonstrate that proportional–derivative–acceleration (PDA) feedback generally, but not always, results in larger stability margins than proportional–derivative (PD) feedback in the presence of reflex delays.

scholarly journals Multiple periodic solutions for a class of second-order nonlinear neutral delay equations

2006 ◽  
Vol 2006 ◽  
pp. 1-9 ◽  
Author(s):  
Xiao-Bao Shu ◽  
Yuan-Tong Xu
Keyword(s):  
Periodic Solutions ◽  
Index Theory ◽  
Second Order ◽  
Delay Equations ◽  
Group Index ◽  
Neutral Delay ◽  
Variational Structure ◽  
Multiple Periodic Solutions ◽  
T Tau

By means of a variational structure andZ2-group index theory, we obtain multiple periodic solutions to a class of second-order nonlinear neutral delay equations of the formx″(t−τ)+λ(t)f(t,x(t),x(t−τ),x(t−2τ))=x(t),λ(t)>0,τ>0.

scholarly journals Variational Methods for Almost Periodic Solutions of a Class of Neutral Delay Equations

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
M. Ayachi ◽  
J. Blot
Keyword(s):  
Variational Methods ◽  
Periodic Solutions ◽  
Delay Equations ◽  
Delay Equation ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Neutral Delay ◽  
Density Result

We provide new variational settings to study the a.p. (almost periodic) solutions of a class of nonlinear neutral delay equations. We extend Shu and Xu (2006) variational setting for periodic solutions of nonlinear neutral delay equation to the almost periodic settings. We obtain results on the structure of the set of the a.p. solutions, results of existence of a.p. solutions, results of existence of a.p. solutions, and also a density result for the forced equations.

State-dependent neutral delay equations from population dynamics

2014 ◽  
Vol 69 (4) ◽  
pp. 1027-1056 ◽  
Author(s):  
M. V. Barbarossa ◽  
K. P. Hadeler ◽  
C. Kuttler
Keyword(s):  
Population Dynamics ◽  
Delay Equations ◽  
Neutral Delay ◽  
State Dependent

scholarly journals Semi-Hyperbolic Mappings, Condensing Operators, and Neutral Delay Equations

1997 ◽  
Vol 137 (2) ◽  
pp. 320-339 ◽  
Author(s):  
A.A Al-Nayef ◽  
P.E Kloeden ◽  
A.V Pokrovskii
Keyword(s):  
Delay Equations ◽  
Neutral Delay ◽  
Condensing Operators
Sign in / Sign up

Export Citation Format

Share Document